In this paper, we present an approach called the free lens modulation (FLM) method to generate high-perfection 3D generalized perfect optical vortices (GPOVs) with topological charges of 1–80. In addition, 2D and 3D GPOVs were produced by altering the parameters of the freely shaped lenses. To verify the quality of the GPOVs produced with the FLM method, we conducted optical trapping experiments and realized linear control of the rotation rate of the trapped particle. Due to the great advantages of high perfection and high power usage in generating arbitrarily shaped GPOVs, the FLM method is expected to be applied in optical manipulation, optical communications, and other fields.